Systems of Quasilinear Parabolic Equations with Discontinuous Coefficients and Continuous Delays

Classical solutions of quasilinear parabolic systems on two dimensional domains

Using a classical theorem of Sobolevskii on equations of parabolic type in a Banach space and recently obtained results on elliptic operators with discontinuous coefficients including mixed boundary conditions we prove that quasilinear parabolic systems in diagonal form admit a local, classical solution in the space of p–integrable functions, for some p > 1, over a bounded two dimensional space...

Remarks on the Dirichlet and State-constraint Problems for Quasilinear Parabolic Equations

We prove two different types of comparison results between semicontinuous viscosity suband supersolutions of the generalized Dirichlet problem (in the sense of viscosity solutions theory) for quasilinear parabolic equations: the first one is an extension of the Strong Comparison Result obtained previously by the second author for annular domains, to domains with a more complicated geometry. The...

Quasilinear Parabolic Functional Evolution Equations

Based on our recent work on quasilinear parabolic evolution equations and maximal regularity we prove a general result for quasilinear evolution equations with memory. It is then applied to the study of quasilinear parabolic differential equations in weak settings. We prove that they generate Lipschitz semiflows on natural history spaces. The new feature is that delays can occur in the highest ...

A Quasilinear Parabolic Equation With Inhomogeneous Density and Absorption

On the convergence of difference schemes for a heat conduction equation

THERE is an extensive literature on difference methods of solving equations of the parabolic type. A considerable proportion of the studies concerns equations with constant coefficients. In a number of papers (see, for example, [l]-[6]) the stability and convergence of schemes with continuous and sufficiently smooth coefficients are studied. For example, in [4] the convergence and stability in ...